Formal Logic

Why do some statements necessarily imply others - and why do even the strongest formal systems have limits? Logic offers the tools to answer these questions with precision, clarity, and depth.This book provides a rigorous yet accessible introduction to logical reasoning, from propositional and predicate logic to modal logic and non-classical logics. It develops the central concepts, methods, and procedures in a clear and structured way, focusing not only on formal rules but on the understanding of structure, meaning, and inference.Classical topics such as equivalences, normal forms, and resolution are complemented by algorithmic methods for automated reasoning and a detailed treatment of Gödel's incompleteness theorems. Readers will also encounter modern perspectives, including modal logic, fuzzy logic, default logic, and answer set programming.With numerous exercises and carefully explained solutions, this book is ideal for anyone who wants to think more clearly, argue more precisely, and gain a deeper understanding of the foundations of mathematics and computer science.